But Koeman has fanned the flames by suggesting the Belgium international will have to move on to fully realise his talent.

"I gave him confidence and he has himself recognised that it was good for his development to play another year at Everton," he told Belgian newspaper HLN.

"There is a very good contact and appreciation between us. What after this season comes, no one knows.

"If Romelu was to play at Everton until the end of his career I know he has left something (behind). His potential is greater and higher than Everton as a final destination."

Koeman likened Lukaku to former Holland striker Patrick Kluivert in terms of talent and career path.

"Kluivert was also a striker who was quite young (when he was) in the picture and had a fantastic career. Eventually Kluivert played for Barcelona, which could happen with Lukaku.

"I think Lukaku is quite complete. He can hold a ball and be a target man and, because he is tall and physically strong, you can play directly with the long ball.

"Lukaku is potentially a great striker, one who is only 23 years old."

While Lukaku is away on international duty with Belgium some of his team-mates have been stepping up their recovery from injury.

Koeman said midfielder Muhamed Besic is progressing well after knee surgery, having torn an anterior cruciate ligament playing against Manchester United in Wayne Rooney's testimonial in August, while defender Tyias Browning has played twice in the last four days after a year sidelined with a knee problem.